Question

When we analyze the light coming from a distant galaxy, we find a particular absorption line with a wavelength of 1025 nm. This same absorption line in light from the sun has a wavelength of 625 nm. Calculate the magnitude of the velocity of the galaxy relative to us.

Answer 1

The velocity of the galaxy relative to us is calculated using the redshift formula with the observed change in wavelength of an absorption line. The calculated velocity is found to be 1.92 x 10^8 m/s, indicating the galaxy is moving away from us.

Step-by-step explanation:

To calculate the velocity of the galaxy relative to us, we can use the redshift formula which relates the change in wavelength of light to the speed of the galaxy as it moves away. The formula is given by v = c * z, where v is the velocity, c is the speed of light, and z is the redshift. The redshift z can be found using the formula z = (Δλ)/(λrest), where Δλ is the change in wavelength and λrest is the rest wavelength.

Let's calculate the redshift first. The change in wavelength Δλ is 1025 nm - 625 nm = 400 nm. So z becomes z = 400 nm / 625 nm = 0.64. Now, if we multiply the redshift z by the speed of light c (approximately 3 x 108 m/s), we find the velocity v of the galaxy:

v = c * z = 3 x 108 m/s * 0.64 = 1.92 x 108 m/s

Therefore, the galaxy is moving away from us at a velocity of 1.92 x 108 m/s.